We were given this problem in physics. Here is an explanation:
This is a standard principle of physics. See the image. A (hypothetical) light wave front from a source far away is incident on a solid wall. The wave crests are for the purposes of this demonstration parallel. The waves that hit the wall are stopped or reflected, and the remaining ones keep going as before:
Not really. The next figure shows what’s wrong with that interpretation. Considering the light wave as an electrical and magnetic field traveling through space, then the arrow points to a place adjacent to the electrical field that is vacant. The electric field will propagate into this space.
See the next figure. The wave front adjacent to the edge of the wall will curve toward the available space, effectively bending the wave front.
Here’s the result of this action. If you take a metal plate and make a small hole in it and then aim a beam of light at the hole, some light will pass through the hole. If the light is monochromatic, and you place a screen to the right of the plate in the figure, then you will see that the illumination on the screen conforms to the graph in the next figure. I copied this figure from Wikipedia and did some slight editing:
Well and good. Now suppose you use electrons (or protons) instead of light waves. The same thing happens. See the next figure:
These electrons (electrons are round and black) and are headed for the hole in single file, but when they emerge from the hole they spread out like shot from the muzzle of a shotgun. Why?
The standard answer is that on a certain level electrons, in fact all particles and even macro objects, behave like waves. We were given the problem of deriving the diffraction of electrons (any sub-atomic particle for that matter).
While I was taking the course I went around and bought up a bunch of other physics books. One of them had a novel way of approaching this problem. It did not involve treating the electrons as waves. How else can you derive the diffraction pattern without resorting to wave analysis? I will give a hint later this week.
Enough of this. The answer lies in application of the Heisenberg uncertainty principle. Also in paying attention. This Quiz Question was resolved in a previous post, which discusses the diffraction of particles due to Heisenberg’s uncertainty principle.